Today's passenger jets travel the shortest (northern) route, which takes them over Iceland, Greenland, and Newfoundland.
However, that's where the Hindenburg would have encountered the Westerlies, blowing in the opposite direction. I don't think it was capable of rising to sufficient altitude to avoid them.
The trade winds blow well south of that latitude. The southern route is considerably longer.
I haven't been able to find any charts so far.